PLEASE HELP ASAP! VERY IMPORTANT AND I NEED TO KNOW NOW! WILL MARK BRAINLIEST AND GIVE 10 POINTS!

Gordon and Tess are trying to determine whether ΔABC and ΔFGE can be proven congruent through rigid motions.

Gordon says that ΔABC ≅ ΔFGE because ΔABC can be reflected over the line x = 1 to create ΔFGE.

Tess says ΔABC ≅ ΔFGE because ΔABC can be translated by the rule (x + 5, y - 7) to create ΔFGE.

Who is correct?

A. Gordon only
B. Tess only
C. Both Gordon and Tess
D. Neither Gordon nor Tess

  D. Neither Gordon nor Tess

Step-by-step explanation:

The vertices ABC are in clockwise order. The corresponding vertices FGE are also in clockwise order. On this basis, you can say that there cannot be a single reflection (as across x=1), because that would reverse the order to counterclockwise. Gordon cannot be correct.

The left-right orientation of vertices A and C is reversed to a right-left orientation for corresponding vertices F and E. This means two reflections or a rotation is involved. Translation cannot reverse the orientation like this, so Tess cannot be correct.

ΔFGE and ΔABC are a reflection of each other across the origin, equivalent to the two reflections "across the x-axis" and "across the y-axis." This is also equivalent to a rotation of 180° about the origin.

Neither Gordon nor Tess is correct.

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